Daan Huybrechs

This PhD position at KU Leuven focuses on nonlinear approximation with multivariate rational functions and their applications. The research will be conducted within the NUMA research section of the Department of Computer Science, one of Europe's largest numerical analysis groups. The project aims to advance the field by developing new tools for rational functions of several variables, addressing the challenging problem of best approximation using multivariate rational functions. This work is expected to have transformative impact across disciplines, with specific research goals including the numerical representation of rational functions, development of numerical algorithms for nonlinear rational approximation, and applications in model order reduction and nonlinear eigenvalue problems. Recent progress in the field has leveraged tensor decomposition techniques to improve the robustness of the pAAA algorithm. The project is designed to build on these advances, exploring several research paths within the expertise of the principal investigators. The NUMA section offers a vibrant academic environment, with over 40 researchers working on a variety of numerical topics. The successful candidate will contribute to both research and didactical tasks within the group. Applicants should hold a master's degree in mathematics, mathematical engineering, or an equivalent programme, and demonstrate interest in mathematical research and motivation to pursue a PhD. The position is funded by an initial scholarship for one year, with the possibility of extension to four years following a positive evaluation. KU Leuven is committed to diversity, inclusion, and equal opportunity, providing a supportive environment for all researchers. To apply, candidates should use the KU Leuven jobsite application link provided. For further information, contact Prof. dr. ir. Daan Huybrechs or Prof. dr. ir. Karl Meerbergen via email. The application deadline is June 15, 2026.